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**SpringFan25** Subsititute C = a + bY into the first expression.

$\displaystyle Y = a + bY + I + G$

$\displaystyle Y(1-b) = a + I + G$

$\displaystyle Y = \frac{a + I + G}{1-b}$

So an increase of £1 to G will cause an increase of $\displaystyle \frac{1}{1-b}$ in Y. Hence the multiplier is $\displaystyle \frac{1}{1-b}$

**Why is this an equilibrium?**

if you are interested in understanding this; You can think of the model as trying to find a level of national production (Y) at which there is exactly enough demand (C + I + G) to consume the production.